To determine the domain and range of the function $g$ from the provided graph:

1. Domain:

• The domain represents all the possible $x$-values for which the function is defined.
• From the graph, the function starts at $x = -3$ and ends at $x = 3$, indicating that the function is defined between these two points.

Thus, the domain in interval notation is: $[-3, 3]$

2. Range:

• The range represents all the possible $y$-values the function can take.
• The highest point on the graph occurs at $y = 1$, and the lowest point occurs at $y = -5$.

Thus, the range in interval notation is: $[-5, 1]$

Would you like more details or have any further questions?

Here are five related questions to further your understanding:

1. How would you determine the domain and range of a function algebraically without a graph?
2. Can a function have an infinite domain or range? How would that affect the graph?
3. What is the significance of a function’s maximum and minimum values in its range?
4. How would you express the domain and range if the function had breaks or holes in the graph?
5. How does the domain of a quadratic function compare to the domain of a rational function?

Tip: When analyzing graphs, always check the endpoints carefully. Open circles mean the point is excluded, while closed circles mean it is included in the domain or range.